Advanced modulation techniques and access technologies are enabling high speed mobile access for users. However, these techniques are increasing the complexity of the development of radio transceivers. The continued quest for flexible and dynamic networks challenges designers to develop novel radio systems capable of processing multi-band and frequency aggregated multi-standard, multi-carrier communication signals. While radio systems designers could use multiple power amplifiers (PA) 10, 12, each one dedicated to a particular radio frequency (RF) band, as shown in FIG. 1, this solution dramatically increases the deployment cost of the network and limits network flexibility. Alternatively, a more suitable solution for future communication systems is the use of a unique multi-band PA 14 to amplify combined multi-band multi-carrier and multi-standard signals, as shown in FIG. 2. This would incur lower costs for materials and more flexibility in deployment. However, this solution imposes new efficiency and linearity challenges. In fact, a single multi-band PA should provide RF performance (efficiency, gain, output power) comparable to multiple single-band PA modules. In addition, when concurrently driven with multiple signals scattered over spaced frequencies, a multi-band PA can actually aggravate the distortion problems encountered.
Previous efforts to improve the efficiency and linearity of single-band PAs, such as load (Doherty) and drain-supply (envelope tracking) modulations, have been applied to improve efficiency at the back-off region of single-band PAs. Recent studies identified sources of bandwidth limitations and devised solutions to mitigate them. Several proof-of-concept prototypes have demonstrated excellent efficiency in the back-off region over a wide range of frequencies.
On the other hand, linearization techniques, such as Digital Pre-distortion (DPD), have been applied to extend the linear region of single-band PAs. A number of DPD schemes have been developed which have demonstrated excellent linearization capability. These schemes evolved from low complexity schemes (e.g., memory-less polynomials, Hammerstein and Wiener models, memory polynomials) to more comprehensive ones (e.g., Volterra series and Artificial Neural Networks (ANN)).
In the case of the Volterra series, its application to the linearization of single-band PAs which exhibit significant memory effects was conditional on its successful pruning. This motivated researchers investigating multi-band DPD schemes to discard the Volterra series option, worrying it would lead to unmanageable and impractical solutions. Hence, most of the recent work has concentrated on efforts to generalize the previously mentioned low complexity schemes to the dual-band PA context.
A dual-band signal can be expressed as follows:
                                                                        x                ⁡                                  (                  t                  )                                            =                            ⁢                                                                    x                    1                                    ⁡                                      (                    t                    )                                                  +                                                      x                    2                                    ⁡                                      (                    t                    )                                                                                                                                          =                                ⁢                                  Re                  ⁡                                      (                                                                                                                                                      x                              ~                                                        1                                                    ⁡                                                      (                            t                            )                                                                          ⁢                                                  ⅇ                                                                                    jω                              1                                                        ⁢                            t                                                                                              +                                                                                                                                  x                              ~                                                        2                                                    ⁡                                                      (                            t                            )                                                                          ⁢                                                  ⅇ                                                                                    jω                              2                                                        ⁢                            t                                                                                                                )                                                              ,                                                          (        1        )            where x(t) is the combined dual-band dual-standard signal, x1(t) and x2(t) are single-band multicarrier signals modulated around the angular frequencies ω1 and ω2, respectively, and {tilde over (x)}1(t) {tilde over (x)}2(t) denote the baseband envelops of x1(t) and x2(t), respectively.
The dual-band input signal can be represented as a broadband signal with an angular carrier frequency equal to (ω1+ω2)/2 as given by:
                                                                        x                ⁡                                  (                  t                  )                                            =                            ⁢                                                                    x                    1                                    ⁡                                      (                    t                    )                                                  +                                                      x                    2                                    ⁡                                      (                    t                    )                                                                                                                          =                            ⁢                              Re                (                                                      (                                                                                                                                                      x                              ~                                                        1                                                    ⁡                                                      (                            t                            )                                                                          ⁢                                                  ⅇ                                                      j                            ⁢                                                                                                                            ω                                  1                                                                -                                                                  ω                                  2                                                                                            2                                                        ⁢                            t                                                                                              +                                                                                                                                  x                              ~                                                        2                                                    ⁡                                                      (                            t                            )                                                                          ⁢                                                  ⅇ                                                      j                            ⁢                                                                                                                            ω                                  2                                                                -                                                                  ω                                  1                                                                                            2                                                        ⁢                            t                                                                                                                )                                    ⁢                                      ⅇ                                          j                      ⁢                                                                                                    ω                            1                                                    +                                                      ω                            2                                                                          2                                            ⁢                      t                                                                      )                                                                                                        =                                ⁢                                  Re                  (                                                                                    x                        ~                                            ⁡                                              (                        t                        )                                                              ·                                          ⅇ                                              j                        ⁢                                                                                                            ω                              1                                                        +                                                          ω                              2                                                                                2                                                ⁢                        t                                                                              )                                            ,                                                          (        2        )            where {tilde over (x)}(t) is the baseband envelope of the combined signal. When the dual-band signal is amplified by a PA, the passband component of the output signal, ypb(t), can be described as:
                                                                                          y                  pb                                ⁡                                  (                  t                  )                                            =                            ⁢                                                                    y                    1                                    ⁡                                      (                    t                    )                                                  +                                                      y                    2                                    ⁡                                      (                    t                    )                                                                                                                          =                            ⁢                              Re                (                                                      (                                                                                                                                                      y                              ~                                                        1                                                    ⁡                                                      (                            t                            )                                                                          ⁢                                                  ⅇ                                                      j                            ⁢                                                                                                                            ω                                  1                                                                -                                                                  ω                                  2                                                                                            2                                                        ⁢                            t                                                                                              +                                                                                                                                  y                              ~                                                        2                                                    ⁡                                                      (                            t                            )                                                                          ⁢                                                  ⅇ                                                      j                            ⁢                                                                                                                            ω                                  2                                                                -                                                                  ω                                  1                                                                                            2                                                        ⁢                            t                                                                                                                )                                    ·                                      ⅇ                                          j                      ⁢                                                                                                    ω                            1                                                    +                                                      ω                            2                                                                          2                                            ⁢                      t                                                                      )                                                                                                        =                                ⁢                                  Re                  (                                                                                                              y                          ~                                                pb                                            ⁡                                              (                        t                        )                                                              ·                                          ⅇ                                              j                        ⁢                                                                                                            ω                              1                                                        +                                                          ω                              2                                                                                2                                                ⁢                        t                                                                              )                                            ,                                                          (        3        )            where y1(t) and y2(t) are multicarrier output signals modulated around the angular frequencies ω1 and ω2 respectively, and {tilde over (y)}1(t) {tilde over (y)}2(t) denote the baseband envelopes of y1(t) and y2(t), respectively.
In the classical PA behavioral modeling approach, the PA behavior is modeled as a single-input single-output (SISO) system where the PA output {tilde over (y)}pb(t) is a function of the PA input {tilde over (x)}(t), as given in (4):{tilde over (y)}pb(t)={tilde over (f)}({tilde over (x)}(t))  (4)where {tilde over (f)} is the SISO describing function of the PA 16, as shown in FIG. 3. Note that the output shown in FIG. 3 is idealized. Digitization of the SISO model requires sampling both {tilde over (x)}(t) and {tilde over (y)}pb(t) at a high frequency rate as follows:
            f              s        ,        SiSo              ≥          (              S        +                  5          ·                      max            ⁡                          (                                                                    B                    1                                    2                                ,                                                      B                    2                                    2                                            )                                          )        ,where B1 and B2 represent the bandwidths of {tilde over (x)}1(t) and {tilde over (x)}2(t), respectively, and S denotes the frequency spacing between the two signals
      (                  i        .        e        .            ,              =                                            f              2                        -                          f              1                                =                                                    ω                2                            -                              ω                1                                                    2              ⁢              π                                            )    ,and where f1 and f2 are the two bands' carrier frequencies, respectively. The factor of 5 represents the spectrum regrowth due to PA nonlinearity which is assumed equal to 5.
Alternatively, a dual-input dual-output (DIDO) approach would require a significantly lower sampling rate. In such a formulation, the PA output in each band (i.e.,{tilde over (y)}1(t) and {tilde over (y)}2(t), is expressed separately as a function of the two input signals' envelopes {tilde over (x)}1(t) and {tilde over (x)}2(t), as given by:{tilde over (y)}1(t)={tilde over (f)}1({tilde over (x)}1(t), {tilde over (x)}2(t)){tilde over (y)}2(t)={tilde over (f)}2({tilde over (x)}1(t), {tilde over (x)}2(t))   (5)where {tilde over (f)}1 and {tilde over (f)}2 form the PA's 18 dual-band describing functions, as shown in FIG. 4. Note that the output shown in FIG. 4 is idealized. Actual output depends on the success of the pre-distortion approach employed. The construction of the two describing functions, {tilde over (g)}1 and {tilde over (g)}2, needed to model and/or to linearize the dual-band PA, is performed in the digital domain This requires the sampling of {tilde over (x)}1(t), {tilde over (x)}2(t), {tilde over (y)}1(t) and {tilde over (y)}2(t) at a frequency rate given byfs,DiDo≧(5·max(B1,B2))
This sampling rate is independent of the frequency separation, S, which may be very large. Hence, fs,DiDo is significantly lower than fs,SiSo. For example, if we assume a dual-band signal composed of a 15 MHz WCDMA signal around 2.1 GHz and a 10 MHz LTE one centered at 2.4 GHz, the theoretical sampling frequency needed for the dual-band model, fs,DiDo, has to be at least equal to 75 MHz; significantly lower than the 675 MHz sampling frequency required for the SISO model. The ratio between the two sampling frequencies is equal to
            f              s        ,        SiSo                    f              s        ,        DiDo              =      0.11    .  
There have been several attempts to devise describing functions in order to implement a dual-band model as given in equation (5). Some have proposed a third order frequency selective pre-distortion technique to handle each band separately in order to model and/or linearize PAs exhibiting strong “differential” memory effects (i.e., high imbalance between the upper and lower in-band and inter-band distortion components). This technique was tested using a multi-carrier 1001 WCDMA signal and extended to address the 5th order inter-modulation distortions of a PA driven with multi-tone signals. Although this technique was applied to multicarrier single-band signals, it can be generalized to the dual-band case provided the required sampling rate is reduced to cope with large frequency spacing.
Some have proposed an IF dual-band model implementing a Weiner-Hammerstein DPD scheme using a sub-sampling feedback path. Although the reported simulation results showed 10 dB spectrum regrowth reduction, the proposed architecture involved digital to analog conversion (DAC) and analog to digital conversion (ADC) with disproportionate sampling rates and complicated IF processing. Furthermore, starting with a 5th order memoryless model driven with a dual-band signal, some have shown that the PA's output in each band depends on both PA input signals. This observation has been generalized to the memory polynomial model to yield a two dimension DPD (2D-DPD) model. Reported linearization results demonstrated a 12 dB improvement of the adjacent channel leakage ratio (ACLR) at the cost of a large number of coefficients. However, stability issues were reported.
Some have proposed an orthogonal representation to handle the ill-conditioning problem and numerical instability of the 2D-DPD model. Alternatively, some have proposed 2D Hammerstein and 2D Weiner models to address the large number of coefficients required by the 2D-DPD model. When applied to construct a behavioral model of a dual-band PA with a nonlinearity order equal to 5 and a memory depth equal to 5, the 2D Hammerstein and 2D Weiner models needed 40 coefficients in each band as opposed to the 2D-DPD which required 150 coefficients. However, while the 2D-DPD model has been validated as a dual-band digital pre-distorter, the application of the 2D Hammerstein and 2D Weiner models to the linearization of dual PAs is problematic and only behavioral modeling results have been reported.
Some have pointed out the implementation complexity of the 2D-DPD and have suggested a two dimensional look up table (LUT)-based representation as an alternative. This latter approach was further simplified to use single dimension LUTs. When applied to the linearization of a dual-band PA driven with dual-band signals (separated by 97 MHz), the model demonstrated an ACLR of about −45 dB, which barely passes the mask. However, the proposed DPD scheme was operated with a sampling rate equal to 153.6 MHz and consequently a large oversampling rate with a 10 MHz signal. Hardware to achieve such a large oversampling rate is costly and undesirable.
Known behavior modeling and linearization approaches have been restricted to generalizing low complexity schemes for single-band PAs. Volterra series have been avoided due to the perceived unmanageable number of coefficients and consequent complexity.